My battery charger has a 2 A and 10 A option. What's the difference? If 10 A is more and faster, why not just put the 10 A option?
You're right that 10 amperes is faster, by a factor of 5x.
Lead-acid batteries are charged in 3 stages, first by constant current (with voltage limit), then by constant voltage (with tapering current), then in the end during float charge the voltage is reduced to a float charge voltage level.
The 2 ampere and 10 ampere options allow charging different capacity batteries. You would use 10 amperes on a car battery and 2 ampere on whatever small batteries you might want to charge that still use the same voltage. For example, a motorcycle battery could use the 2 ampere charging option. Many lead-acid batteries only allow 25% of the capacity per hour: 2 amperes could then be used to charge at least 8 amp-hour batteries, whereas 10 amperes could be used to charge at least 40 amp-hour batteries.
I'm not sure how good your charger is, but many these days are microprocessor controlled, so they have all of the 3 stages. The very best are temperature compensated.
In the worst case, the charger doesn't have a sane voltage limit and thus requires you to observe the charging time and disconnect the charger when you expect the battery to be full of charge.
TLDR: use 2A when unattended.
An ideal battery charger does 3-stage charging based on the battery voltage - to quickly charge in the midrange, taper the charge near full, and then trickle at the right rate once full. This requires a fair amount of intelligence in the charger.
Overcharging damages the battery. (Lots of things damage lead-acid batteries, looking at them cross-eyed damages them).
This is a cheaper battery charger that doesn't have that onboard intelligence. Instead, it lets you manually switch rates. If you will be monitoring the charge actively, you can punch up the 10A rate. If you will be walking away from it for hours or days, select 2A and that will better approximate the trickle charging it should get when full, so you will do less damage.
That battery charger has been designed to charge smaller, and larger, 12V batteries.
The ones on motorcycles or batteries having a smaller capacity need a lower charging rate.
However, if the charger is a quality one, then it will have a charge control circuit that will change the charging regime according to the state of charge of the battery - most good ones do this.
There are also "fast" chargers that will charge at 50 or 60A to boost a flat battery so it will start a car. Used once is usually ok if the battery is not already damaged, but if used on the same battery for long periods it damages the battery.